A denotational semantics of a parallel object-oriented language
Pierre America, J.W. deBakker, Joost N. Kok, Jan J. M. M. Rutten · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · 1985
A denotational model is presented for the language POOL, a parallel objectoriented language.It is a syntactically simplified version of POOL-T, a language that is actually used to write programs for a parallel machine.The most important aspect of this language is that it describes a system as a collection of communicating objects that all have internal activities which are executed in parallel.To describe the semantics of this language we construct a mathematical domain of processes.This domain is obtained as a solution of a reflexive domain equation over a category of complete metric spaces.A new technique is developed to solve a wide class of such equations, including function space constructions.The desired domain is obtained as the fixed point of a contracting functor implicit in the equation.The domain is sufficiently rich to allow a fully compositional definition of the language constructs in POOL, including concepts such as object creation and method invocation by messages.The semantic equations give a meaning to each syntactic construct depending on the POOL object executing the construct, the environment constituted by the declarations, and a continuation, representing the actions to be performed after the execution of the current construct.After the process representing the execution of an entire program is constructed, a yield function can extract the set of possible execution sequences from it.A preliminary discussion is provided on how to deal with fairness.Full mathematical details are supplied, with the exception of the general domain construction, which is described elsewhere.